90=n(36-3n+3)

Solution for 90=n(36-3n+3) equation:

90=n(36-3n+3)

We move all terms to the left:

90-(n(36-3n+3))=0

We add all the numbers together, and all the variables

-(n(-3n+39))+90=0


We calculate terms in parentheses: -(n(-3n+39)), so:

n(-3n+39)

We multiply parentheses

-3n^2+39n

Back to the equation:

-(-3n^2+39n)


We get rid of parentheses

3n^2-39n+90=0

a = 3; b = -39; c = +90;
Δ = b2-4ac
Δ = -392-4·3·90
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-39)-21}{2*3}=\frac{18}{6}
=3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+21}{2*3}=\frac{60}{6}
=10
$